Single-site Green-function of the Dirac equation for full-potential electron scattering

Kordt, Pascal

Internal Report

Single-site Green-function of the Dirac equation for full-potential electron scattering

Kordt, P. (Corresponding author)FZJ*

2011
Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag Jülich
ISBN: 978-3-89336-760-3

Jülich : Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag, Schriften des Forschungszentrums Jülich. Schlüsseltechnologien / Key Technologies 34, 138 S. (2011) = RWTH Aachen, Diss., 2011

Please use a persistent id in citations: http://hdl.handle.net/2128/4548

Abstract: I present an elaborated analytical examination of the Green function of an electron scattered at a single-site potential, for both the Schrödinger and the Dirac equation, followed by an efficient numerical solution, in both cases for potentials of arbitrary shape without an atomic sphere approximation. A numerically stable way to calculate the corresponding regular and irregular wave functions and the Green function is via the angular Lippmann-Schwinger integral equations. These are solved based on an expansion in Chebyshev polynomials and their recursion relations, allowing to rewrite the Lippmann-Schwinger equations into a system of algebraic linear equations. Gonzales et al. developed this method for the Schrödinger equation, where it gives a much higher accuracy compared to previous perturbation methods, with only modest increase in computational effort. In order to apply it to the Dirac equation, I developed relativistic Lippmann-Schwinger equations, based on a decomposition of the potential matrix into spin spherical harmonics, exploiting certain properties of this matrix. The resulting method was embedded into a Korringa-Kohn-Rostoker code for density functional calculations. As an example, the method is applied by calculating phase shifts and the Mott scattering of a tungsten impurity.

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